In all of these expressions, IF(z)
and DF(z) are the discrete integrator
formulas for the integrator and derivative filter, respectively. Use
the IFormula and DFormula properties
of the controller objects to set the IF(z)
and DF(z) formulas. The next
table shows available formulas for IF(z)
and DF(z). Ts is
the sample time.

IFormula or DFormula

IF(z) or DF(z)

ForwardEuler (default)

Tsz−1

BackwardEuler

Tszz−1

Trapezoidal

Ts2z+1z−1

If you do not specify a value for IFormula, DFormula,
or both when you create the controller object, ForwardEuler is
used by default. For more information about setting and changing the
discrete integrator formulas, see the reference pages for the controller
objects, pid, pidstd, pid2,
and pidstd2.

Setting Td = 0 specifies a PI controller with no derivative term. As the display shows, the values of N and c are not used in this controller. The display also shows that the trapezoidal formula is used for the integrator.

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